{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:COBTO56MYHFUSSUDMATZDLNZGP","short_pith_number":"pith:COBTO56M","schema_version":"1.0","canonical_sha256":"13833777ccc1cb494a83602791adb933fe97f863363311d25c53114108a26b33","source":{"kind":"arxiv","id":"1009.3318","version":1},"attestation_state":"computed","paper":{"title":"On affine motions and bar frameworks in general position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"A. Y. Alfakih, Yinyu Ye","submitted_at":"2010-09-17T02:33:47Z","abstract_excerpt":"A configuration p in r-dimensional Euclidean space is a finite collection of points (p^1,...,p^n) that affinely span R^r. A bar framework, denoted by G(p), in R^r is a simple graph G on n vertices together with a configuration p in R^r. A given bar framework G(p) is said to be universally rigid if there does not exist another configuration q in any Euclidean space, not obtained from p by a rigid motion, such that ||q^i-q^j||=||p^i-p^j|| for each edge (i,j) of G. It is known that if configuration p is generic and bar framework G(p) in R^r admits a positive semidefinite stress matrix S of rank n"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.3318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-09-17T02:33:47Z","cross_cats_sorted":[],"title_canon_sha256":"40b6911157441694cc76b602d988e094313d0e9a105bb581b2a3851122a7bfc4","abstract_canon_sha256":"e98ccf356e9e7ae4e2eecb193c9759c033f5a8c0d2af5eedb721e1d0d5b09f20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:45.965556Z","signature_b64":"dpz5Z/GmmYxI9fUGV/SYX56lQiLsruqgZoQeT4WOKgYZirfUOZhXl4oJ8niqI1tGkgT5ZxBefxuSMyaGhpNlDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13833777ccc1cb494a83602791adb933fe97f863363311d25c53114108a26b33","last_reissued_at":"2026-05-18T04:40:45.964794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:45.964794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On affine motions and bar frameworks in general position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"A. Y. Alfakih, Yinyu Ye","submitted_at":"2010-09-17T02:33:47Z","abstract_excerpt":"A configuration p in r-dimensional Euclidean space is a finite collection of points (p^1,...,p^n) that affinely span R^r. A bar framework, denoted by G(p), in R^r is a simple graph G on n vertices together with a configuration p in R^r. A given bar framework G(p) is said to be universally rigid if there does not exist another configuration q in any Euclidean space, not obtained from p by a rigid motion, such that ||q^i-q^j||=||p^i-p^j|| for each edge (i,j) of G. It is known that if configuration p is generic and bar framework G(p) in R^r admits a positive semidefinite stress matrix S of rank n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3318","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.3318","created_at":"2026-05-18T04:40:45.964892+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3318v1","created_at":"2026-05-18T04:40:45.964892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3318","created_at":"2026-05-18T04:40:45.964892+00:00"},{"alias_kind":"pith_short_12","alias_value":"COBTO56MYHFU","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"COBTO56MYHFUSSUD","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"COBTO56M","created_at":"2026-05-18T12:26:06.534383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/COBTO56MYHFUSSUDMATZDLNZGP","json":"https://pith.science/pith/COBTO56MYHFUSSUDMATZDLNZGP.json","graph_json":"https://pith.science/api/pith-number/COBTO56MYHFUSSUDMATZDLNZGP/graph.json","events_json":"https://pith.science/api/pith-number/COBTO56MYHFUSSUDMATZDLNZGP/events.json","paper":"https://pith.science/paper/COBTO56M"},"agent_actions":{"view_html":"https://pith.science/pith/COBTO56MYHFUSSUDMATZDLNZGP","download_json":"https://pith.science/pith/COBTO56MYHFUSSUDMATZDLNZGP.json","view_paper":"https://pith.science/paper/COBTO56M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3318&json=true","fetch_graph":"https://pith.science/api/pith-number/COBTO56MYHFUSSUDMATZDLNZGP/graph.json","fetch_events":"https://pith.science/api/pith-number/COBTO56MYHFUSSUDMATZDLNZGP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/COBTO56MYHFUSSUDMATZDLNZGP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/COBTO56MYHFUSSUDMATZDLNZGP/action/storage_attestation","attest_author":"https://pith.science/pith/COBTO56MYHFUSSUDMATZDLNZGP/action/author_attestation","sign_citation":"https://pith.science/pith/COBTO56MYHFUSSUDMATZDLNZGP/action/citation_signature","submit_replication":"https://pith.science/pith/COBTO56MYHFUSSUDMATZDLNZGP/action/replication_record"}},"created_at":"2026-05-18T04:40:45.964892+00:00","updated_at":"2026-05-18T04:40:45.964892+00:00"}